Realization of equilibrium points by means of a completely symmetrical nonlinear circuit

An associative memory circuit is one of the main applications of mutually coupled neural networks, which can be realized by the analog circuits composed of resistors, capacitors and operational amplifiers with saturation characteristics. These analog circuits have therefore extensively been investigated from the viewpoint of both the nonlinear circuit theory and the neural network theory. This paper studies on the realization of a set of equilibrium points by means of this type of circuits. In the conventional realization of associative memory circuits many spurious equilibrium points in addition to desired equilibrium points inevitably appear. It is therefore desirable to give a method of synthesizing a circuit with desired equilibrium points only. As the first step to the above purpose we consider a simple circuit with completely symmetrical structure. The assumptions we impose on the circuit make the weight matrix very simple so that all diagonal elements are identical and all nondiagonal elements are identical. We also assume that the characteristics of each operational amplifier can be represented by a 3-segment piecewise linear function. We first give the characterization of a set of equilibrium points and secondly give an algorithm to determine whether or not the prescribed set of equilibrium points can be realized by means of the above simple circuit.